On the Relations between Lucas Sequence and Fibonacci-like Sequence by Matrix Methods
Журнал: International Journal of Mathematical Sciences and Computing(IJMSC) @ijmsc
Статья в выпуске: 4 vol.3, 2017 года.
Бесплатный доступ
In the present paper first and foremost we introduce a generalization of a classical Fibonacci sequence which is called a Fibonacci-Like sequence and at hindmost we obtain some relationships between Lucas sequence and Fibonacci-Like sequence by using two cross two matrix representation to the Fibonacci-Like sequence. The most worth noticing cause of this article is our proof method, since all the identities are proved by using matrix methods.
Fibonacci Sequence
\ Lucas Sequence
\ Generalization of Fibonacci Sequence
\ Matrix Method
Короткий адрес: https://sciup.org/15014274
IDS: 15014274
Список литературы On the Relations between Lucas Sequence and Fibonacci-like Sequence by Matrix Methods
- Cerda, G., “Matrix Methods in Horadam Sequences”, Boletín de Matemáticas, 19(2), 2012, pp.97-106.
- Čerin, Z., “On Factors of Sums of Consecutive Fibonacci and Lucas Numbers”, Annales Mathematicae et Informaticae, 41, 2013, pp. 19-25.
- Dasdemir, A., “On the Pell, Pell-Lucas and Modified Pell Numbers by Matrix Method”, Applied Mathematical Sciences, 5(64), 2011, pp.3173-3181.
- Horadam, A. F., “Basic Properties of a Certain Generalized Sequence of Numbers”, The Fibonacci Quarterly, 3(3), 1965, pp.161-176.
- Jun, S. P. and Choi, K. H., “Some Properties of the Generalized Fibonacci Sequence by Matrix Methods Methods”, The Korean Journal of Mathematics, 24(4), 2016, pp.681-691.
- Keskin, R. and Demirtürk, B., “Some New Fibonacci and Lucas Identities by Matrix Methods”, International Journal of Mathematical Education in Science and Technology, 41(3), 2010, pp.379-387.
- Kilic, E., “Sums of Generalized Fibonacci Numbers by Matrix Methods”, Ars Combinatoria, 84, 2007, pp.23-32.
- Koken, F. and Bozkurt, D., “On Lucas Numbers by the Matrix Method”, Hacettepe Journal of Mathematics and Statistics, 39(4), 2010, pp.471-475.
- Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, 2011.
- Posamentier, A. S., The Fabulous Fibonacci Numbers, Prometheus Books, 2007.
- Singh, B., Bhadouria, P. and Sikhwal, O., “Generalized Identities Involving Common Factors of Fibonacci and Lucas Numbers”, International Journal of Algebra, 5(13), 2011, pp.637-645.
- Thongmoon, M., 2009, “Identities for the Common Factors of Fibonacci and Lucas Numbers”, International Mathematical Forum, 4(7), 2009, pp. 303-308.
- Vajda, S., Fibonacci and Lucas Numbers and the Golden Section: Theory and Applications, Courier Corporation, 1989.